Remarks on some dispersive estimates

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On the Cauchy Problem of Fractional Schrödinger Equation with Hartree Type Nonlinearity (2012, background): “We first consider the standard Strichartz estimate for the unitary group U(t) (see [10]):”
Strichartz Estimates in Spherical Coordinates (2012, background): “It is obvious that the range and the exponents are sharp ([12]).”
On Fractional Schrodinger Equations in sobolev spaces (2015, background): ““ ż Rd 1 2 ||∇|σupt,xq|2 ` µ p`1 |upt,xq|p`1dx. (energy). FRACTIONAL SCHRODINGER 3¨ An important feature of the equation under study is a loss of derivatives for the Strichartz estimates as proved in [COX11]. Unless additional assumptions are met such as radiality as in [GW14], one has a loss of dp1”